1st Grade - Gateway 1

The materials reviewed for Imagine Learning Illustrative Mathematics Grade 1 meet expectations for assessing grade-level content and if applicable, content from earlier grades. The materials for Grade 1 are divided into eight units, and each unit contains a written End-of-Unit Assessment. Additionally, the Unit 8 Assessment is an End-of-Course Assessment, and it includes problems from the entire grade level. Examples of End-of-Unit Assessments include: 

• Unit 2, Addition and Subtraction Story Problems, End-of-Unit Assessment, Problem 5, students “Circle 3 true equations. A. 5+4=9, B. 3=8+5, C. 4=10=6 D. 9-8=1 E. 7+1=6.” (1.OA.7)

• Unit 3, Adding and Subtracting Within 20, End-of-Unit Assessment, Problem 3, “Elena scored 8 points in a basketball game. Noah scored 5 points, and Diego scored 2 points.How many points did Elena, Noah, and Diego score together? Show your thinking using drawings, numbers, or words.” (1.OA.2, 1.OA.3) 

• Unit 5, Adding Within 100, End-of-Unit Assessment, Problem 1, students “Find the value of each sum. a. 46+10. b. 46+20. c. 46+50.” (1.NBT.4, 1.NBT.5)

• Unit 7, Geometry and Time, End-of-Unit Assessment, Problem 6, students demonstrate “a. What time is shown on the clock? b. Draw the clock hands to show the time.” The clock hands show 4:30, and the digital clock shows 8:00. (1.MD.3)

The materials reviewed for Imagine Learning Illustrative Mathematics Grade 1 meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards. The materials provide extensive work with and opportunities for students to engage in the full intent of Grade 1 standards by including in every lesson a Warm Up, one to three instructional activities, and Lesson Synthesis. Within Grade 1, students engage with all CCSS standards.

Examples of extensive work include:

• Unit 2, Unit 4, and Unit 8 engage students in extensive work with 1.NBT.1 (Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.) In Unit 2, Addition and Subtraction Story Problems, Lesson 8, Shake, Spill, and Cover, Warm-up: Choral Count: Count On From 10, students count numbers to 40. “‘Count by 1, starting at 10.’ Record as students count. Stop counting and recording at 40. ‘What patterns do you see?’” In Unit 4, Numbers to 99, Lesson 19, Make Two-digit Numbers, Activity 3: Centers: Choice Time, students choose from activities that offer practice working with two-digit numbers. “‘Now you are going to choose from centers we have already learned.’ Display the center choices in the student book.” Student Task Statements, “Choose a center. Greatest of Them All (71, 75). Get Your Numbers in Order. 14, 36, 82. Grab and Count.” Lesson Synthesis, “‘Today we made two-digit numbers in different ways. We used different amounts of tens and ones to make the same number.’ Display 3 tens and 7 ones, 2 tens and 17 ones, 1 ten and 27 ones, 37 ones. ‘Which do you think best matches the two-digit number 37? Why do you think it matches the number best? (3 tens and 7 ones matches best because the digits in the number tell us that there are 3 tens and 7 ones. 37 ones matches best because the number is read ‘thirty-seven.’).’” In Unit 8, Putting it All Together, Lesson 7, Count Large Collections, Warm-up: What Do You Know About 103? Teacher Guide, “Display the number. ‘What do you know about 103? How could we represent the number 103?’” Activity 1: Last Number Wins, students count within 120 starting at a number other than 1. “Display chart with “start” and “stop” numbers. ‘Today we are playing a new game called Last Number Wins. In this game your group will count from the ‘start’ number to the ‘stop’ number. The person to say the last number wins. Let’s play one round together. Our ‘start’ number will be 1 and our ‘stop’ number will be 43.’” 

• Unit 3, Adding and Subtracting Within 20, Lesson 3, Are the Expressions Equal?, Activity 1, Sort Addition Expressions, engages students in extensive work with 1.OA.3 (Apply properties of operations as strategies to add and subtract.) Students sort addition expressions by their value. Teacher Guide, “Give students their addition expression cards. Sort the cards into groups with the same value. Display an addition expression card, such as 2+5. ‘I know the value of this sum is seven. It is a sum that I just know. I will start a pile for sums of seven. Work with your partner. Make sure that each partner has a chance to find the value before you place the card in a group. If you and your partner disagree, work together to find the value of the sum.’” Activity 2: Are Both Sides Equal?, students determine whether equations are true or false. Student Task Statements, “Determine whether each equation is true or false. Be ready to explain your reasoning in a way that others will understand. 1.) 4+2=2+4. 2.) 3+6=6+4. 3.) 5+3=1+7. 4.) 6+4=5+3. 5.) 6+3=9+2.” Lesson 16, Add Three Numbers, Warm-up: Number Talk: Related Expressions, students use strategies and understandings students have for adding on to. Teacher Guide, “Display one expression. Give me a signal when you have an answer and can explain how you got it.” Student Task Statements, “Find the value of each expression mentally. 7+10, 7+2+8, 10+9, 4+9+6.”

• Unit 4, Numbers to 99, Lessons 16, and 17, engages students with extensive work with 1.NBT.3 (Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <). Lesson 16, Write Comparisons with Symbols, Activity 2: Make the Statement True, students practice writing symbols that make a comparison statement true. “Compare the numbers. Write <, >, or = in each blank. Then read the comparison statement. a. 56__26, b. 72__78, c.$$6__55$$, d. 92__29, e. 23__23”. In Lesson 17, Compare and Order Numbers, Warm-up, students evaluate comparison statements and decide which statements are true or false based on their base ten knowledge. “‘Which one doesn’t belong? a. 5<30, b. 25<35, c. 35<20, d. 30>20, How do you know that C is false? (35 isn't less than 20 because 35 has 3 tens and 20 only has 2 tens.), What could you change about C to make it true?’ (Use the greater than symbol or switch the symbol around.)”

Examples of full intent include:

• Unit 3, Adding and Subtracting Within 20, Lessons 9 and 10 engage students in the full intent of 1.OA.8 (Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8+?=11, 5=___-3, 6+6=___). In Lesson 9, Addition With a Ten, Cool-down, students are asked to determine the unknown whole number in addition equations. “Find the number that makes each equation true. Show your thinking using drawings, numbers, or words. 1. 10+9=___, 2. 10+___=12.” In Lesson 10, Addition and Subtraction with a Ten, Cool-down, students are asked to determine the unknown whole number in addition and subtraction equations. “Find the number that makes each equation true. 1. 16-10=___, 2. 19=10+____, 3. 17- __=7 Choose one equation.”

• Unit 6, Length Measurements Within 120 Units, Lesson 1, Compare Lengths, and Lesson 2, Compare the Length of Objects Indirectly, students engage with the full intent of 1.MD.1 (Order three objects by length; compare the lengths of two objects indirectly by using a third object.) Students order 3 objects from shortest to longest and longest to shortest in Activity 2. Students are provided a collection of objects, “Required Preparation- Each group of 4 needs 10-12 objects to measure (thin classroom objects like pencils, crayons, paper clips, toothpicks, markers) including connecting cube towers of 3, 5, and 8.” Students use these objects to respond to the following task, “1. Pick 3 objects. With your partner, put the objects in order from shortest to longest. Trace or draw your objects. 2. Pick 3 new objects. With your partner, put them in order from longest to shortest. Write the names of the objects in order from longest to shortest.” In Lesson 2, Compare the Length of Objects Indirectly, students use string to measure objects that cannot be lined up end to end to make comparisons about their length. The Teacher Guidance for the Launch directs teachers to say, “We saw that sometimes we can compare length without lining up the objects. Now, you are going to compare the length of a side of your desk to the length of one of the legs of your desk.” Teachers then display an image of a desk indicating where to measure the side and where to measure the leg and say, “‘This image shows which side we will be measuring. Trace the length of the side you will measure with your finger.  Why is it important that everybody knows which side of the desk we should measure? Does it matter which leg of the desk you measure?’ (One side is longer than the other, so we need to make sure we are measuring the same thing. All the legs are the same length, so it shouldn’t matter which one we measure.)” Students complete, “Compare the length of the side of your desk and the length of one of the legs of your desk using the string. Use a drawing or words to explain how you know which is longer.” Section A Practice Problems also provide students with an opportunity to compare the length of objects. Problem 4 shows an image of different length rectangles labeled A, B, C, “Use any tool you would like to compare the length of the rectangles. List the rectangles from longest to shortest.” Problem 5 has students compare the length of objects indirectly, “Compare the length of the top and side of your workbook. Use a drawing or words to show which is longer.”

• Unit 7, Geometry and Time, Lessons 14, 15, and 16, students engage with the full intent of 1.MD.3 (Tell and write time in hours and half-hours using analog and digital clocks.) In Lesson 14, Half of the Clock, Activity 2: Half Past What? students identify whether a clock is showing a time that’s half past or o’clock. Teacher Guide, “Give each student a red and a blue colored pencil, crayon, or marker. Display clock cards for 9:00 and half past 9. ‘Which card shows 9 o’clock and which card shows half past 9?’ Student Task Statements, ‘What time is shown on each clock? If the time is half past, color the clock red. If the time is o’clock, color the clock blue. Write the time in words using half past or o’clock.’Cool-down: Find 2:30, ‘Circle the clock that shows 2:30.’” In Lesson 15, Write Times, Activity 2: All the Time in the World, students write time to the hour and half hour based on clocks with one or both hands. Teacher Guide, “Give students their Half Past Clock Cards. ‘Write the times on the new clock cards that show half past.’ Student Task Statements, ‘1. For each clock, write the time. 2. For each clock, draw the minute hand and write the time. 3. This clock only has a minute hand. What time could it be? If you have time: What other times can you show on the clock?’” In Lesson 16, Hard Times, Cool-Down Draw the Clock, Problem 1, students see a picture of an analog clock showing 6:00 and 12:30 and a picture of a blank digital clock. “Show the time on each clock.”

The materials reviewed for Imagine Learning Illustrative Mathematics Grade 1 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of the grade. The instructional materials devote at least 65 percent of instructional time to the major clusters of the grade: 

• The approximate number of units devoted to the major work of the grade (including assessments and supporting work connected to major work) is 7 out of 8, approximately 88%.

• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to major work) is 141 lessons out of 154 lessons, approximately 92%. The total number of lessons include 133 lessons plus 8 assessments for a total of 141 lessons. 

• The number of days devoted to major work of the grade (including assessments and supporting work connected to major work) is 152 days out of 162 days, approximately 94%.

The lesson-level analysis is the most representative of the instructional materials, as the lessons include major work, supporting work connected to major work, and assessments in each unit.  As a result, approximately 92% of the instructional materials focus on major work of the grade.

The materials reviewed for Imagine Learning Illustrative Mathematics Grade 1 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. 

Materials are designed with supporting standards/clusters connected to the major standards/clusters of the grade. These connections are listed for teachers on a document titled, “Pacing Guide and Dependency Diagram” found on the Course Guide tab for each Unit. Teacher Notes also provide the explicit standards listed within the lessons. Examples of connections include:

• Unit 1, Adding, Subtracting, and Working with Data, Section C Practice Problems, Problem 3, connects the supporting work of 1.MD.4 (Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another) to the major work of 1.OA.6 (Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten ; decomposing a number leading to a ten ; using the relationship between addition and subtraction ; and creating equivalent but easier or known sums. Students use a tally chart to count, add, and answer questions. “a. How many students chose dogs? b. How many students chose birds? c. How many students chose dogs or cats? d. How many students chose cats or birds?”

• Unit 2, Addition and Subtraction Story Problems, Lesson 13, Compare Favorite Art Supply Data, Activity 2 connects the the supporting work of 1.MD.4 (Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another) to the major work of 1.OA.1 (Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.) Students are shown survey results and asked, “What is your favorite art supply?” They use the data to answer questions including, “1. How many more students voted for crayons than for paint?, Show your thinking using drawings, numbers, or words., 2. How many fewer students voted for markers than paint? Show your thinking using drawings, numbers, or words.” 

• Unit 7, Geometry and Time, Lesson 15, Write Times, Activity 1, Count the Minutes, connects the supporting work of 1.MD.3 (Tell and write time in hours and half-hours using analog and digital clocks) to the major work of 1.NBT.1 (Count to 120, starting at any number less than 120). Students tell and write time in hours and half-hours using analog and digital clocks. Student Task Statements, students are shown a clock. “Start at 12. Count the minutes around the clock until you get to half the clock. Circle where you stop.”

The materials reviewed for Imagine Learning Illustrative Mathematics Grade 1 meet expectations for including problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade. 

Materials are coherent and consistent with the Standards. Examples of connections between major work to major work and/or supporting work to supporting work throughout the materials, when appropriate, include:

• Unit 2, Addition and Subtraction Story Problems, Lesson 5, Center Day 1 connects the major work of 1.OA.A (Represent And Solve Problems Involving Addition And Subtraction) to the major work of 1.OA.C (Add and subtract within 20). In Activity 2: Centers: Choice Time, students choose from activities that offer practice organizing and representing data, telling and solving story problems, and adding and subtracting within 10. In the Teacher Guide Launch, “Now you are going to choose from centers we have already learned.” Display the center choices in the student book. “Think about what you would like to do first.” Student Task Statements, “Sort and Display, Math Stories, or Find the Pair.” 

• Unit 2, Addition and Subtraction Story Problems, Lesson 8, Shake, Spill, and Cover, Activity 2: Shake and Spill, Cover Problems, connects the major work of 1.OA.A (Represent and solve problems involving addition and subtraction) to the major work of 1.OA.D (Work with addition and subtraction equations). In the Student Task Statement, students are asked to “represent and solve Put Together/Take Apart, Addend Unknown story problems.” Students are shown a picture with a few counters they can see and count and some counters hidden under a cup. “1. There are 9 counters total. How many counters are under the cup?”

• Unit 5, Adding Within 100, Lesson 10, Tens and Tens and Ones and Ones connects the major work of 1.NBT.C (Use place value understanding and properties of operations to add and subtract) to the major work of 1.OA.D (Work with addition and subtraction equations). In Activity 2, Finish the Work, students use place value to add. Teacher Guide Launch, “Give students access to connecting cubes in towers of 10 and singles. Read the first problem. 4 minutes: partner work time. “What is the difference between how you solved 28+56 and 27+44. (For 28+56, I added the tens first, then the ones. For 27+44 I added the ones first, then the tens.)” 

• Unit 6, Length Measurements Within 120 Units, Lesson 9, Write Numbers to 120 connects the major work of 1.NBT.A (Extend the counting sequence) to the major work of 1.MD.A (Measure lengths indirectly and by iterating length units. In Activity 2, Write Numbers to Represent Animal Lengths, students write numbers to tell the length of an object. In the Teaching Notes, “Create a poster to show how you counted the cubes you used to measure the length of the animal in the measuring animals activity. Do not write the number of cubes your animal measured on your poster.”

The materials reviewed for Imagine Learning Illustrative Mathematics Grade 1 meet expectations that content from future grades is identified and related to grade-level work and materials relate grade-level concepts explicitly to prior knowledge from earlier grades. 

The Section Dependency Chart explores the Unit sections relating to future grades. The Section Dependency Chart states, “arrow indicates the prior section that contains content most directly designed to support or build toward the content in the current section.” 

Examples of connections to future grades include:

• Unit 4, Numbers to 99, Section A, Units of Ten, Section narrative, connects 1.NBT.1 (Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.), 1.NBT.2 (Understand that the two digits of a two-digit number represent amounts of tens and ones.), 1.NBT.4 (Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction…), 1.NBT.5 (Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.), 1.NBT.6 (Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.) to work done in grade 3. “Because the focus here is on connecting written numbers to their word names and the amounts of tens they represent, terms such as “two-digit number,” “digits,” “multiples,” “tens place,” and “ones place” are not used. “Multiple of 10” is used in teacher-facing text but is not a term that students use until grade 3. Students should be encouraged to use any language that makes sense to them.”

• Unit 6, Length Measurements Within 120 Units, Lesson 8, Groups Up to 110, Warm-up, Choral Count: Above 100, connects 1.NBT.1 (Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral) to work in grade 2. “The purpose of this Choral Count is to invite students to practice counting by 1 from 80 to 110 to prepare them to count large groups of objects later in the lesson. Students will develop an understanding of three-digit numbers and a hundred as a unit in grade 2”.

• Unit 8, Putting It All Together, Lesson 3, About This Lesson connects 1.OA.6 (Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten…) and 1.OA.8 (Determine the unknown whole number in an addition or subtraction equation relating three whole numbers) to work in grade 2. “In previous lessons, students practiced adding and subtracting within 10. In this lesson, students use the methods that make the most sense to them to add and subtract within 20. The lesson activities encourage students to use methods such as using known facts, making 10 to add, decomposing a number to lead to a 10 to subtract, and using the relationship between addition and subtraction. This lesson helps students practice adding and subtracting with 20 and apply their fluency within 10 in preparation for their work with addition and subtraction in grade 2.”

Examples of connections to prior knowledge include:

• Unit 1, Adding, Subtracting, and Working With Data, Lesson 7: Sort Math Tools, About This Lesson connects 1.MD.4 (Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another) to the work of Kindergarten. “In kindergarten, students sorted objects into given categories (K.MD.3). In this lesson, students choose categories to sort tools they have used in previous lessons (pattern blocks, two-color counters, and inch tiles). Students explain how they sorted and how many are in each category. ”

• Unit 2, Additional and Subtraction Story Problems, Unit Overview, Full Unit Narrative, Unit Learning Goals, “In kindergarten, students solved a limited number of types of story problems within 10 (Add To/Take From, Result Unknown, and Put Together/Take Apart, Total Unknown, and Both Addends Unknown). They represented their thinking using objects, fingers, mental images, and drawings. Students saw equations and may have used them to represent their thinking, but were not required to do so.”

• Unit 4, Numbers to 99, Lesson 1, Count Large Collections, About this lesson, connects 1.NBT.1, 1.NBT.2, 1.OA.5, 1.OA.6, 1.OA.8 to work done in kindergarten. “In the previous unit, students learned that a ten is a unit made up of 10 ones. Students learned that teen numbers are made up of 1 ten and some more ones, using 10-frames, drawings, and expressions (10+n). In kindergarten, students learned the counting sequence by ones and tens up to 100. The purpose of this lesson is for teachers to formatively assess how students count objects up to 60 through two counting activities.”